Bridging the gap between one way and two-way shear in slabs
The shear capacity of slabs under concentrated loads is particularly of interest for bridge decks under concentrated live loads. Often, one-way shear will be analyzed by considering the slab as a wide beam (without taking advantage of the transverse load redistribution capacity of the slab) and two-way shear by considering the punching area around the load. Since experiments showed that the failure mode of slabs under concentrated loads is a combination of one-way and two-way shear as well as two-way flexure, a method was sought that bridges the gap between traditional one-way and two-way shear approaches. The proposed method is a plasticity-based method. This method is based on the Strip Model for concentric punching shear and takes the effects of the geometry into account for describing the ultimate capacity of a slab under a concentrated load. The model consists of “strips” that work with arching action (one-way shear) and slab “quadrants” that work in two-way shear. As such, the resulting Extended Strip Model is suitable for the design and assessment of elements that are in the transition zone between one-way and two-way shear.
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Bridging the gap between one way and two-way shear in slabs
- 1. The Concrete Convention andExposition Bridging the gap between one-way and two- way shear in slabs Eva Lantsoght, Cor van der Veen, Ane de Boer, Scott Alexander
- 2. The Concrete Convention andExposition Overview • Introduction: plastic design methods • Strip model for concentric punching shear • Extended Strip Model • Application to Ruytenschildt Bridge • Summary & Conclusions Slab shear experiments, TU Delft
- 3. The Concrete Convention andExposition Plastic design methods • Solutions for – One-way shear – Two-way shear – Flexure • Lower bound methods – Strut-and-tie models – Hillerborg´s strip method • Upper bound methods – Yield line methods Strut-and-tie model of dapped-end beam Mattock, A. H. (2012). "Strut-and-tie Models for Dapped-End beams," Concrete international, 34(2), 35-40.
- 4. The Concrete Convention andExposition Design gap between one-way and two-way shear • One-way shear – beam shear – Over effective width – Beam tests • Two-way shear – punching shear – Over punching perimeter – Slab-column connection tests • Slab bridges under concentrated live loads? S6T4 cracking
- 5. The Concrete Convention andExposition Strip Model for concentric punching shear (1) • Alexander and Simmonds, 1990 • For slabs with concentrated load in middle
- 6. The Concrete Convention andExposition Strip Model for concentric punching shear(2)
- 7. The Concrete Convention andExposition Extended Strip Model(1) • Adapted for slabs with concentrated load close to support • Effect of geometry, continuity, and torsion • Maximum load: based on sum capacity of 4 strips
- 8. The Concrete Convention andExposition Extended Strip Model (2) • Unequal loading of strips in y-direction • Static equilibrium • v1 reaches max before v2 • Reduction for self-weight ' 2 0.166M c x M a v f d L a
- 9. The Concrete Convention andExposition Extended Strip Model (3) • Size effect added • Increase in capacity of strip between load and support • Effect of continuity on moment capacity hogging and sagging reinforcement
- 10. The Concrete Convention andExposition Extended Strip Model (4) • Edge effect: – when length of strip is too small to develop loaded length lw • Effect of torsion
- 11. The Concrete Convention andExposition Extended Strip Model (5) Comparison between Extended Strip Model and slab shear experiments
- 12. The Concrete Convention andExposition Ruytenschildt Bridge (1) • Existing reinforced concrete slab bridge (1962) • Test to failure in two spans • 4 concentrated load – one tandem • Cyclic loading protocol • Failure only achieved in span 2
- 13. The Concrete Convention andExposition Ruytenschildt Bridge (2) Existing bridge Partial demolition and building new bridge
- 14. The Concrete Convention andExposition Ruytenschildt Bridge (3)
- 15. The Concrete Convention andExposition Test results proofloading Span 2• Maximum load 3991 kN • Large flexural cracks • Flexural failure – yielding of reinforcement • Settlement of bridge pier with 1.5cm – Elastic recovery to 8mm • Prediction ESM: 3157 kN • Tested/Predicted = 1.26 • Safe lower bound
- 16. The Concrete Convention andExposition Summary & Conclusions • Extended Strip Model – Plasticity-based model – For analysis of capacity of slabs – One-way shear in strips – Two-way flexure in quadrants – Effect of torsion considered • Case study: Ruytenschildt Bridge – Existing slab bridge scheduled for replacement – Testing in 2 spans, failure in span 2 – Good, safe prediction of ESM
- 17. The Concrete Convention andExposition Contact: Eva Lantsoght E.O.L.Lantsoght@tudelft.nl // elantsoght@usfq.edu.ec +31(0)152787449